Death, being the incarnation of that state, is dead. She enters the realm of Death at will, and when she incarnates as mortal every century, she regains her own personification by dying. As Lovecraft and Martin have said in their own special ways, you cannot die when you are already dead. Death is unique, even among the Endless, for she occupies a paradoxical state - a moving, 'living' manifestation of a concept that embodies the opposite. More so than the other Endless, she is endless and will never give up an incarnation, or a 'point of view', as Despair and Dream have done.
It is proven that she never 'dies', as we see her in Gaiman's The Books of Magic at the end of the universe, overseeing Destiny's end and sending Timothy Hunter back to his own time before she leaves. She is still very much the same Death that we knew in the Sandman series, showing no changes as she would if, like Dream and Despair, she had changed incarnations during the ages past.
There is also mystery of the six cerements. In 'The Wake', when Eblis O'Shaunessy goes into the secret room of the necropolis that holds the funeral cerements of the Endless, we see six hanging in the room. Only Dream's is clearly identified. Since Despair's death used one, the remaining six could be for Destiny, Death, Dream, Destruction, Desire, and Delirium. However, there are other theories on the remaining cerements' owners - if a given Endless can 'die' more than once, Despair's cerement should have been replaced, meaning that the absent cerement would be Death's. (There is also the theory that Destruction, having given up his function, no longer would rate a cerement, but I postulate that he's still one of the Endless though he no longer actively pursues the duties of his role; thus, his cerement should still be there waiting for him.)
Since there is no indication that the Endless are limited to giving up only one incarnation during their existence, I posit that the absent cerement shows that Death, alone among her kin, will always be as we know her, and will never seek oblivion.